To date, the cochineal insect query I posed yesterday have produced
some useful information that I would like to summarize for those who
might be interested.  Thank you for your response.
 
The cochineal is a bright red dye or stain made by drying and
pulverizing the bodies of the females of the small, tropical
American scale insect, 'Dactylopius coccus', that feeds on certain
species of cacti, including prickly pear cactus, and can be found in
in the clumps of white fuzz that it produces on the surface of
cacti.
 
I have been informed (at least on an informal basis, thanks to the
HISTARCH-L folks -- I. Waynne Cox, Brian W. Kenny, Frank Kohout,
Susan L Shaffer Nahmias, Gail Ryser) that the cochineal occurs in
southern Texas and Arizona, and also as far south as Peru, where it
is known to have been utilized during prehistoric times for dying
textiles. Cochineal dye was the Spaniard's third most economically
important export items from the southern Texas region during colonial
times, and near the end of that period it was imported to the Canary
Islands for cultivation; prior to that time, export of the insect was
forbidden, but it was allowed once the Spanish thought they might
lose their New World holdings. The cochineal dye was used to dye wool
that Navajo weavers got from the Spanish and then unravelled, respun
and wove into their textiles.
 
The cochineal insect (female) still is used to produce red-dye stains
for biological research, and it may have been used extensively to
produce red dye for Persian rugs.
 
My equating cochineal with murex was incorrect [the following
information comes from Frank Kohout].  Murex is a salt-water mussel
whose shell is used to produce a royal purple dye.  In ancient times
the Phoenicians were the main producers of murex purple in the
Mediterranean area, and their name even derives from the Greek word
[phoinkeos] for purple/red, the shades of which the Greeks apparently
did not distinguish with different words.
 
There are at least a couple of articles that deal with the cochineal
(I haven't yet made it to the library to read them):
 
Fleming, Stuart
1983 "The Tale of the Cochineal: Insect Farming in the New
World," Science Scope, _Archaeology_, Vol 36, No 5, Sept/Oct,
pp.68-79.
 
According to Waynne Cox, Fleming's article makes a point that the
cultivation of the bugs was about the only industry that the Spanish
left in the hands of the natives, implying that they had been doing
it for a long time before their arrival.
 
Eisner, T., S. Nowicki,M. Goetz and J.Meinwald
"Red cochineal dye [carminic acid]: its role in nature,"_Science_
[208]: 1039-42.
 
A.J. Taylor
Tempe, AZ